Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1909 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C23×C4 |
| direct product | C23×#1910 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #386 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C23×#535 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C22×C4×C23 ◁ G | |
344 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 368 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25)(26,32)(27,35,37,30)(28,34)(29,31)(33,36,39,38);(24,26,32,25,29,34,28,31)(27,33,36,30,37,39,38,35);(24,27)(25,30)(26,33)(28,38)(29,37)(31,35)(32,36)(34,39)667 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#12755, C23×#12758, C23×#12778, … |
| maximal normal subgroup of | C23×#12755, C23×#12758, C23×#12778, … |
| maximal quotient of | C23×#9101, C23×#9102, C23×#9105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 642);